For wireless transmission, pilots or pilot signals are used to identify a channel for each transmit antenna to the receive antennas. The channel is then used in demodulating data symbols. In 3rd Generation Partnership Project (3GPP) long-term evolution (LTE) networks, pilot overhead is approximately 5% per antenna, about 16% for 4 antennas, and even higher for 8 or more antennas. In these types of networks, multiple transmit antennas can be used for diversity to improve received signal power or to send multiple spatial streams, all of which increase transmission throughput. As the number of antennas grows so does the potential for further throughput improvement; however, the overhead due to pilots also grows.
Compressed sensing may reduce pilot overhead and enable cellular systems to increase the number of antennas or improve the effectiveness for a fixed number of antennas. Compressed sensing relies on the assumption that channels can be represented compactly in some basis. Consequently, fewer samples are required to identify the channel relative to traditional methods, such as Nyquist sampling, which requires a sampling rate that is at least twice the highest frequency component of the signal. For example, in contrast to traditional Nyquist sampling, the number of samples needed for compressed sensing is ideally proportional to the amount of information in the signal. Thus, with compressed sensing, the number of samples increases as the amount of information in the signal increases. Consequently, signals having relatively large amounts of information may require a relatively large number of samples to accurately obtain the transmitted data at the receiver.